Aneurysm of aorta and dissection of the aorta are typical diseases of the thoracic aorta, and there is an influential theory that those diseases are caused by aortic wall stress. Especially in relation to aortic aneurysm, magnitude of generated stress and risk of rupture of the aneurysm are considered to be directly related with each other. Decision of whether or not to perform operation has been judged by measuring the diameter of the aneurysm and evaluating the generated stress in the aneurysm based on the Laplace's law (approximation of thin-walled cylindrical shells) (C.f. Non-patent Literature 1) in clinical practice. However, this diagnostic method using only a representative dimension for evaluating stress of a complex shaped aneurysm includes a problem of accuracy, and cases have been reported where rupture occurred at an aneurysm shape to which operation had not been performed under the decision of the above-mentioned diagnostic method (C.f. Non-Patent Literature 2). In this regard, a development of stress evaluation method with higher accuracy is required, and the finite element analysis of individual aortic wall stress analysis is considered as one of the effective means.
Stress analysis of aortic wall has been numerously tried by now. For example, a three-dimensional finite element stress analysis (C.f. Non-Patent Literature 3) reproducing the effect of blood pressure and tensile force caused by the heart assuming the aortic wall as a linear elastic body, and a non-linear finite element analysis (C.f. Non-Patent Literature 4) reproducing blood pressure and tensile force and by using various constitutive laws as material models for the wall of blood vessel of the aorta and by using the shape model generated from the multi sliced CT of human thoracic aorta, have been performed.
However, the foregoing analysis methods have the following problems generally when applied to the bio-mechanical analysis. (a) Since it is impossible for measuring the material property parameters of aorta of each individual in vivo, modification of the experimental data conducted in vitro using a typical specimen is needed before the use. (b) Since it is also impossible for obtaining the shape of aorta under a non-loaded condition from CT images, some analysis must be done to modify the shape which was obtained from a loaded condition or a kind of residual stress must be introduced.
Conventional stress analysis methods caused by the analysis complexity and uncertainty in accordance with above problems will hardly become a practical diagnostic tool in the scene of clinical practice. On the other hand, an alternative approach for evaluating stress of the aortic wall by avoiding above problems has been tried. For example, there is a method of calculating maximum stress value only from the internal pressure and curvilinear shape (C.f. Non-Patent Literature 5) by assuming that the flexural rigidity of the blood vessel wall can be ignored, and using an axisymmetric model as an approximation of abdominal aneurysm of aorta, and there is also another attempt (C.f. Non-Patent Literature 6) extending this calculation method to a quasi-axisymmetric curvilinear surface.